To the right hand side of each row of your table, enter the formula "=max()" and select the row of numbers to go inside the brackets above (e.g. a2:e2)
That will create a sixth column of 18 numbers, each the maximum of their row.
To find the sum of these numbers use the formula "=sum()" and inside the brackets, select the cells that contain the row maximums.
Does that make sense to you?
Can't think of any easy way to highlight the maximum in each row off the top of my head - but I do have a very cumbersome way if you really want to do it.